The mitral valve annulus is an anatomical structure joining the leaflets and left ventricle wall. It is divided into the fibrous annulus in the anteromedial section and the myocardium annulus in the posterolateral section, according to annulus histology. Two trigones are in the fibrous annulus. Mitral annulus supports leaflets in the valve coaptation and controls inflow hemodynamics during a cardiac cycle. When the mitral valve is fully open during diastole, inflow drag force on the leaflets and chordae pulls the leaflets approximately apically. As mitral valve leaflets coaptate during systole, trans-mitral pressure acts on the leaflets and induces leaflet tension which is transferred to the annulus and chordae. The leaflet tension at the annulus per unit length is defined as annulus tension (AT). Annulus dilatation is a mitral valve pathology that is related to AT and its interaction with the myocardium. Little is known about the detailed mechanism of annulus dilatation. But from mechanics standpoint, there are two possible mechanisms that change annulus size. AT pulls annulus towards the center of mitral valve orifice and is balanced by myocardium force on the annulus that pulls the annulus outward. Annulus size depends upon which force is predominant in annulus mechanics. It is hypothesized that the AT is one of the important mechanism to control annulus size. This hypothesis suggests that annulus size can be controlled by the AT and its interaction with the myocardium. We aim to understand annulus dilatation by the AT. The objective of the current study was to understand the tension transferred to the mitral annulus by the leaflets during the valve coaptation.

Ventricular assist devices (VADs) have received widespread application to treat adults with end-stage heart failure. However, application to the pediatric population has been limited due to the excessive size; and therefore miniature, pediatric VADs (PVADs) are now being developed for the pediatric population to expand the current treatment options available to young patients with congenital heart defects and acquired heart disease. These pumps are typically connected via the left ventricular apex (via an inflow cannula) to the ascending aorta (via an outflow cannula). The distal anastomosis between outflow cannula and aorta has been studied by other researchers [1, 2] revealing complex fluid dynamic phenomena due to the non-physiologic confluence of native blood flow and outflow from the VAD. The corresponding pediatric anastomosis differs in dimensions and proportions to the adult, and has not yet been studied. The objective of this initial study is to examine the influence of cannula design, location, angle of insertion, and flow rate on the macro- and micro-fluid dynamics in the pediatric aorta. This parametric study is intended to provide both developers and surgeons with insight that would lead to optimization of both the cannula and surgical procedure, with particular emphasis at avoiding recirculation and stagnation flows commonly associated with platelet activation and thrombus generation [2, 3].

Pathobiological studies have demonstrated that atherosclerotic lesions have been found on the wall of saccular cerebral aneurysms [1]. We propose a hypothesis that some of these aneurysms are prevented from rupturing due to the atherosclerotic lesions. It has been presented that mass transport of biochemical species such as LDL and ATP, has some important roles in the development of atherosclerosis. A variety of Computational Fluid Dynamics (CFD) studies of the mass transport has been performed for arteries [2, 3], few studies have however, done for aneurysms.

Intracranial aneurysms are pathological dilations of the arteries in the brain, whose rupture is often fatal. Surgery and endovascular embolization are the two most common methods of treatment. Surgery involves opening a portion of the skull and placing metallic clips at the aneurysm neck thereby preventing blood flow into the aneurysm. In the case of embolization, a catheter is used to pack platinum coils in the aneurysm reducing the inflow and promoting thrombus formation. Due to its less invasive approach endovascular embolization is preferred over surgery. Nevertheless this approach also has some serious aftereffects. Coil compaction followed by the re-growth or the formation of the secondary aneurysm is the most common problem. The endovascular embolization approach also has a serious shortcoming that the coils alone cannot be used to block every type of aneurysm. Wide neck or fusiform aneurysms are coiled with the help of stents. Recent studies show that stent, which is a hollow cylindrical mesh, can be successfully used to limit the flow of blood into the aneurysm. However these studies have been conducted using idealized in-vitro and numerical models. Studies conducted using patient-specific models generated from medical images will provide a more realistic approach to computationally investigate the effects of stents on intra-aneurysmal flow patterns. However generation of computational grids inside the parent vessel and around these stents is a challenging task. In this paper an algorithm to map the stent to a patient-specific vascular model and an adaptive unstructured embedded gridding technique to model flow around stents are presented. Finally these techniques are demonstrated on patient-specific cases to prove their feasibility.

A numerical method is presented for calculating 3-D unsteady flow through bileaflet heart valves and flexible obstruction. The method combines finite volume, finite element, and overlapping grid methods. The employed overlapping grid method decomposed the entire domain into the solid region, the fluid region in the vicinity of the solid (the inner region), and the outer fluid region. A finite volume scheme was implemented for the outer fluid region, while a finite element scheme was employed in the solid and inner fluid regions. Calculations were carried out for the full 3-D valve geometry under steady inflow conditions with the Reynolds number ranging from 400 to 1200. The numerical results illustrate the evolution of the downstream vortices. The changes in the location and size of the reattachment vortices in response to the change of elastic modulus of solid and Reynolds number of fluids were recorded and tabulated. The results provide the detailed information sketching the evolution of the fluid-structure interaction in terms of the modes and amplitude.

Central venous catheters (CVCs) are used as a way to provide adequate access of blood flow for hemodialysis, a common treatment for end-stage kidney disease. During hemodialysis, the catheter must circulate up to 300 mL/min [1] of blood flow to the extracorporeal artificial kidney. Catheters contain two lumens: the inflow lumen provides flow to the artificial kidney, and the outflow lumen returns it to the patient’s circulation. Although catheters are used in the treatment of patients of all ages, this study is motivated by the use of central venous catheters for pediatric applications; the catheter types and calibers available for children are much more limited than for adults, thereby placing children in a further disadvantage and potentially subjecting them to increased risk of complications.

Due to the growing shortage of donor livers, more patients are waiting for liver transplantation. Efforts to expand the donor pool include the use of living donor liver transplantation (LDLT) and split liver transplantation. LDLT involves a healthy person undergoing a partial hepatectomy to donate a part of his liver to a patient with severe liver failure. Afterwards, the regenerative capacity of the organ allows the livers of both donor and recipient to regrow to normal liver masses. The procedure is not without risk as serious complications may occur (such as cholestasis, ascites, gastrointestinal bleeding and renal impairment). An inadequate liver mass compared to the body mass may result in the small-for-size syndrome (SFSS). In both donor and recipient, LDLT may lead to portal hypertension associated with the elevated intrahepatic resistance of a smaller liver, and an increased portal venous (PV) inflow per gram of liver tissue compared to the total liver before resection. Excessive hyperperfusion and shear stress may damage the sinusoidal endothelial cells and lead to graft dysfunction.

Abdominal Aortic Aneurysm (AAA) is a common disease among Caucasian males above the age of 60 and its rupture is the 10 th leading cause of death in the U.S. [1] An AAA is commonly defined as a 50% local increase in diameter of the normal infrarenal aorta, and is located below the renal arteries and the iliac bifurcation. At present the measured maximum diameter or the rate of increase of the diameter over time are used as clinical parameters to judge the suitability of surgical intervention to prevent rupture. As a clinical diagnosis rule, aneurysms with diameter less than 4 cm are kept under periodic surveillance and between 5 cm and 6 cm, or expansion rates greater than 1 cm / year, are recommended for surgical or endovascular intervention. Unfortunately, retrospective studies reveal that about 33% of ruptured aneurysms had a maximum diameter less than 5 cm at the time of the rupture [2]. This demonstrates that the correlation between a critical diameter and rupture risk assessment of AAAs has its limitations and thus opens the opportunity for further research on other critical parameters that may be suitable for future diagnosis and rupture prediction. Our ongoing computational efforts [3] focus on this issue as we propose the use of patient specific fluid-structure interaction (FSI) models to investigate the potential of individual flow-induced wall stress as a key biomechanical parameter that can be used for rupture risk evaluation. In this work we report on the setup of the computational protocol for patient specific analysis and assess the effect of modeling parameters on the derivation of individual inflow and outflow boundary conditions for AAA fluid flow simulation and validation.

Numerical simulations of blood flow in the human cardiovascular system are usually performed using custom Finite element methods and specialized boundary conditions. These simulations are performed to (a) understand the physics of blood flow in the human cardiovascular system and (b) a priori testing of proposed treatments/interventions whether surgical or endovascular. To perform these simulations, we require prior knowledge of parameters such as cardiovascular geometry, boundary conditions (inflow/outflow/pressure), etc. In the past, researchers have assumed exact values for these parameters. However, in reality, each of these parameters is uncertain. For example, inflow conditions into the model are dictated by the heart rate and cardiac output of the patient. Even during rest, there are variations in cardiac output and hence the corresponding blood inflow velocities need to be modeled as a random variable. Additionally, the cardiovascular geometry is built based on MRI-images. These are subject to uncertainties due to noise in the data and variability between users during model construction. We develop a computational toolbox that can account for uncertainties in such parameters in hemodynamic simulations. The uncertainties examined in this work include i) variation and accuracy of image-based model geometry ii) variability in inflow condition of the patient and iii) variability in the implementation of the final surgical design. The last source of uncertainty stems from the fact that optimally designed surgical parameters may not be exactly implemented in the operating room. We show numerical examples of (a) blood flow in stenotic vessels (b) effect of uncertainty in carotid sinus size on blood flow and (iii) develop a stochastic optimization technique to compute optimal parameters of an idealized Y-graft model for the Fontan surgery accounting for sources of uncertainties listed above.

Computational models enable the calculation of quantities that are impractical or impossible to measure and the prediction of physiological changes due to interventions. In order to be useful, cardiovascular models must be both rooted in physical principles and designed such that measured or otherwise desired features of the cardiovascular system are reproduced. The former requirement has motivated the development of image-based anatomic models, patient-specific inflow boundary conditions, deformable vascular walls, outflow boundary conditions that represent the influence of the downstream circulation, and multiscale models. The development of approaches to address the latter requirement, reproducing desired features of the circulation, is a critical area of modeling research that has received comparatively little attention.

The endovascular deployment of inferior vena cava (IVC) filters is a clinical treatment for the prevention of pulmonary embolism due to deep vein thrombosis. In addition, IVC filters are used routinely for prophylactic purposes in patients who are at high risk of developing pulmonary embolism, e.g., trauma patients. There are approximately eight IVC filters available in the U.S., each with a unique design.

Rupture of abdominal aortic aneurysm (AAA) is the 10 th leading cause of death for men over age of 50 in US. The decision for surgical intervention is currently based on aneurysm diameter or its expansion rate. However, the use of these criteria for all patients is debatable. For example, small aneurysms do rupture or become symptomatic before reaching the critical diameter. Computationally predicted mechanical wall stress is considered a viable alternative criterion for rupture risk assessment. Hence, it is important to evaluate the effect of different modeling approaches on the accuracy of the predicated AAA wall stress. For computational solid stress (CSS) analysis or finite element analysis (FEA), a uniform static or transient intraluminal pressure is generally applied on the wall-lumen surface whereas in fluid-structure interaction (FSI) modeling the wall-lumen surface experiences transient and non-uniform fluid stress. An earlier comparison on idealized AAA models [1] revealed that static and transient CSS underestimate the peak wall stress (PWS) by an average 20–30% for variable wall thickness and 10% for uniform wall thickness when compared to fully coupled FSI. However, FSI-predicted stresses and strains were observed to be sensitive to inflow and outflow boundary conditions, warranting further study on a more accurate approach for FSI modeling. Though significant work has been performed on modeling outflow boundary conditions [2], studies on the sensitivity of computed stress or strain to the type of FSI inflow boundary condition is scarce [2–4]. We hypothesize that a FSI framework with a patient specific velocity boundary condition derived from magnetic resonance imaging (MRI) data applied to patient specific AAA geometry would provide better accuracy of PWS calculations compared to a FEA model. In this work, we present a framework where the AAA geometry is reconstructed from computed tomography (CT) images, on which FSI simulations were performed with inlet velocity components extracted from patient MR images of the abdominal aorta. Fully coupled FSI simulations were performed and results were compared with CSS simulations with uniform transient pressure boundary conditions.

Wide-neck and giant cerebral aneurysms are difficult to treat with conventional endovascular or surgical means [1]. Recently, stand-alone stent treatment has been explored as a viable treatment option for these aneurysms. Two goals of standalone stent design are to permit flexible conformation of the stent through tortuous vessels and to provide sufficient coverage across the aneurysmal neck [2]. Stents that achieve those goals can facilitate the long-term physiological processes that exclude the aneurysmal sac from circulation. Thrombosis within the sac is an important intermediate step, which may begin with the elimination of aneurysmal inflow [3].

It has been demonstrated that computational fluid dynamics (CFD) have the potential to enhance the comprehension of the role played by hemodynamic factors involved in atherosclerosis. Recently, phase-contrast magnetic resonance imaging (PC-MRI) has emerged as an effective tool for providing accurate vascular geometries for CFD simulations and quantitative data on blood flow rates, which can be used to specify realistic boundary conditions (BCs). However, the application of acquired flow waveforms at boundaries is not straightforward, mainly (i) due to possible occurrences of phase shifts and attenuations of outflow with respect to inflow rate and (ii) due to the instantaneous mass conservation constraint, which is required in hemodynamic simulations with rigid wall models, but is not guaranteed in in vivo measurements. As an alternative, new boundary conditions schemes have been developed in an effort to consider the interaction between the computational domain and the upstream/downstream vasculature by coupling through-scale hemodynamic models [1]. However, the identification of the parameters of these simplified vascular models on a subject-specific base involves both pressure and flow rates measurements [2]. In this context, it is clear that the direct application of individual PC-MRI measured flow rates waveforms as BCs in patient-specific simulations should be preferred [3]. In order to overcome the limitations mentioned above, measured flow rates should be combined with stress-free conditions or fixed mass flow ratio (derived from the same set of PC-MRI data) between inlet and multiple outlet sections. However, prescribing different BCs at boundaries can affect the solutions of the equations governing blood flow [1]. For this reason, different strategies in combining outlet BCs could lead to different simulated hemodynamics. This work analyzes the influence of different possible strategies of applying PC-MRI measured flow rates on an image-based hemodynamic model of a healthy human aortic arch with supra-aortic vessels. A total of six flow simulations was carried out applying six different schemes for treating BCs at outlets. Three common wall shear stress (WSS)-based indicators of abnormal flow were considered and the sensitivity of these indicators to the outlet treatment strategy was evaluated.

Atherosclerotic lesions have a highly non-uniform distribution in regions of arterial branching and curvature, consistent with hemodynamic factors, in particular wall shear stress (WSS), controlling their development. The widespread and increasing use of the mouse as a model for studying atherosclerosis has encouraged investigation of the hemodynamics of the mouse aortic arch [1–3], in which previous studies have revealed areas of high and low lesion prevalence and variation in the expression of pro-atherogenic molecules [4]. Our previous computational simulations [1–2] did not produce distributions of WSS that explain the pattern of lesions. We are currently investigating whether incorporation of more realistic aortic root velocity measurements, obtained using phase-contrast magnetic resonance imaging (PC-MRI), into these simulations can improve the correlation with disease. Here we present velocities obtained by PC-MRI and preliminary simulations employing the data.

Unbalanced distribution of hepatic blood flow to the lungs in single ventricle patients can result in the formation of harmful arterial-venous shunts. Careful planning of the hepatic baffle placement to optimize its distribution can help to minimize this risk. The combination of in vivo imaging, a computational fluids solver, and a state-of-the-art virtual surgery interface have successfully been demonstrated to assist in this planning step. In the present study, we analyze the effect of the patient-derived flow boundary conditions on the optimal solutions obtained from the simulations for a particular set of complex cases with interrupted inferior vena cava. By considering two patients with similar anatomical configurations but drastically different hemodynamics, we see that differences in the percentage of cardiac output carried by each of the inflow vessels can drastically alter the optimal surgical approach.